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Comment on a Paper by Tahara on the Finite Subgroups of GL(3,Z)

Published online by Cambridge University Press:  22 January 2016

E. Ascher  and
H. Grimmer
E. Ascher
Affiliation:
Battelle, Advanced Studies Center
H. Grimmer
Affiliation:
Battelle, Advanced Studies Center
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Tahara [1] has concretely determined the conjugate classes of finite subgroups of GL(3, Z). The group W5 in his list of groups of order 24 is in fact of order 12 and consists of the same matrices as the group W6 in his list of groups order 12. Hence, there are only 10 conjugate classes of subgroups of order 24 in GL(3, Z) and the total number of conjugate classes of finite subgroups is reduced to 73.

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Other
Information
Nagoya Mathematical Journal , Volume 48 , December 1972 , pp. 203
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

References

[1] Tahara, K.-I., On the Finite Subgroups of GL (3, Z), Nagoya Math. J. Vol. 41 (1971), p. 169–210.CrossRefGoogle Scholar
[2] Zassenhaus, H., Über einen Algorithmus zur Bestimmung der Raumgruppen, Comment. Math. Helv. Vol. 21 (1948), p. 117–141.CrossRefGoogle Scholar
[3] Niggli, P., Nowacki, W., Der arithmetische Begriff der Kristallklasse und die darauf fussende Ableitung der Raumgruppen, Z. Kristallographie Vol. A91 (1935), p. 321–335.Google Scholar
[4] Wondratschek, H., Bülow, R., Neubüser, J., On Crystallography in Higher Dimensions. III. Results in R4 . Acta Cryst. Vol. A27 (1971), p. 523–535.CrossRefGoogle Scholar